We report on the first calculation of the structure function g_1 in polarised deep-inelastic scattering to the third order in massless perturbative QCD. The calculation follows the dispersive approach already used for the corresponding unpolarised ca
ses of F_2,L, but additionally involves higher tensor integrals and the Dirac matrix gamma_5 in D unequal 4 dimensions. Our results confirm all known two-loop expressions including the coefficient functions of Zijlstra and van Neerven not independently verified before. At three loops we extract the helicity-difference next-to-next-to-leading order (NNLO) quark-quark and gluon-quark splitting functions Delta P_qq and Delta P_qg. The results exhibit interesting features concerning sum rules and the momentum-fraction limits x to 1 and x to 0.
We calculate the next-to-next-to-leading order ${cal O}(alpha_s^4)$ one-loop squared corrections to the production of heavy quark pairs in quark-antiquark annihilations. These are part of the next-to-next-to-leading order ${cal O}(alpha_s^4)$ radiati
ve QCD corrections to this process. Our results, with the full mass dependence retained, are presented in a closed and very compact form, in the dimensional regularization scheme. We have found very intriguing factorization properties for the finite part of the amplitudes.
Third-order results for the structure functions of charged-current deep-inelastic scattering are discussed. New results for 11th Mellin moment for F_2,L^(nu P - nubar P) structure functions and 12th moment for F_3^(nu P - nubar P) are presented as we
ll as corresponding higher Mellin moments of differences between the respective crossing-even and -odd coefficient functions. Approximations in Bjorken-x space for these differences obtained with lowest five moments as well as consistency of new results with these approximations are discussed. The 1/N_c suppression of the differences is shown and the correction to the Paschos-Wolfenstein relation is discussed.
Second- and third-order results are presented for the structure functions of charged-current deep-inelastic scattering in the framework of massless perturbative QCD. We write down the two-loop differences between the corresponding crossing-even and -
odd coefficient functions, including those for the longitudinal structure function not covered in the literature so far. At three loops we compute the lowest five moments of these differences for all three structure functions and provide approximate expressions in Bjorken-$x$ space. Also calculated is the related third-order coefficient-function correction to the Gottfried sum rule. We confirm the conjectured suppression of these quantities if the number of colours is large. Finally we derive the second- and third-order QCD contributions to the Paschos-Wolfenstein ratio used for the determination of the weak mixing angle from neutrino-nucleon deep-inelastic scattering. These contributions are found to be small.
We report on our recent results for deep-inelastic neutrino-proton scattering. We have computed the perturbative QCD corrections to three loops for the harged current structure functions F_2, F_L and F_3 for the combination nu P - nubar P. In leading
twist approximation we have calculated the first six odd-integer Mellin moments in the case of F_2 and F_L and the first six even-integer moments in the case of F_3. As a new result we have obtained the coefficient functions to O(alpha_s^3) and we have found the corresponding anomalous dimensions to agree with known results in the literature.
We derive for deep-inelastic neutrino-proton scattering in the combination nu P - nubar P the perturbative QCD corrections to three loops for the charged current structure functions F_2, F_L and F_3. In leading twist approximation we calculate the fi
rst five odd-integer Mellin moments in the case of F_2 and F_L and the first five even-integer moments in the case of F_3. As a new result we obtain the coefficient functions to O(alpha_s^3) while the corresponding anomalous dimensions agree with known results in the literature.
